Bivariate macromodeling with guaranteed uniform stability and passivity

This paper extends the well-established macromodeling flows based on rational fitting and passivity enforcement to the bivariate case, where the model response depends on frequency and on some additional design parameter. We propose a black-box model identification algorithm that is able to guarantee uniform stability and passivity throughout the parameter range. The resulting models, which can be cast as parameterized SPICE subnetworks, may be used to construct parameterized component libraries for design optimization, what-if analyses and fast parametric sweeps in frequency or time domain.